Coastal Carolina Heating and Cooling Inc. has a $6-$month backlog of orders for its patented solar heating system. To meet this demand, management plans to expand production capacity by $45\%$ with a $$20$ million investment in plant and machinery. The firm wants to maintain a $35\%$ debt level in its capital structure. It also wants to maintain its past dividend policy of distributing $55\%$ of last year$$s net income. In $2021,$ net income was $$5$ million. How much external equity must Coastal Carolina seek at the beginning of $2022$ to expand capacity as desired? Assume that the firm uses only debt and common equity in its capital structure.